Final answer to the problem
$2\ln\left|x-1\right|-\ln\left|x+3\right|+C_0$
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Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x+7)/(x^2+2x+-3))dx. Rewrite the expression \frac{x+7}{x^2+2x-3} inside the integral in factored form. Rewrite the fraction \frac{x+7}{\left(x-1\right)\left(x+3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2}{x-1}+\frac{-1}{x+3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{x-1}dx results in: 2\ln\left(x-1\right).
Final answer to the problem
$2\ln\left|x-1\right|-\ln\left|x+3\right|+C_0$
